BOSTON — Amid a rousing standing ovation for Elizabeth Warren from hundreds of teachers here Saturday, the concern Massachusetts and national Democrats have about the state of the Harvard University professor’s Senate campaign seemed far away.

Warren has stumbled to recover from the revelation that she intermittently claimed Native American ancestry during her academic career. But among her base at the Massachusetts Teachers Association’s annual meeting of delegates, the support for Warren was strong and unwavering. When she took the stage at the Hynes Convention Center, the candidate was received with booming applause that would have been louder if dozens of teachers hadn’t been snapping photos with their cellphones.

The worry among Democrats is not so much that this controversy will be an issue that sinks her campaign or moves that many voters — it won’t, and polls show Warren neck and neck with GOP Sen. Scott Brown. But rather, her reaction to it reveals an operation that may not be agile enough to deal with the vicissitudes of a hard-fought battle in the national spotlight.

Warren, the presumptive Democratic nominee, didn’t mention the prickly issue of her heritage during her speech.

While coverage of the flap has begun to subside almost three weeks after the story first broke, it hasn’t gone away.

One top Massachusetts Democratic strategist who is an ally of the campaign groused that if Warren’s camp didn’t know she had claimed Native American ancestry for years, they were guilty of “incompetence,” and if they knew and didn’t prepare her properly for the onslaught of questions, they were guilty of “malpractice.”

Former Massachusetts Attorney General Scott Harshbarger, who was the Democratic nominee for governor in 1998, said Warren was doing very well but that the controversy revealed miscalculations within her campaign apparatus.

“The campaign came to rely an awful lot on her ability and probably that was expecting too much,” he said, noting she was a first-time politician. Warren is “a candidate who is just learning how to handle these kind of curveballs, and that’s where you, as a campaign, whether it’s [campaign manager] Mindy Myers or [senior adviser] Doug Rubin ... have to dig deeper so they knew more about this or just be aware that these kind of things are coming.”

Evan Bayh, a former Democratic Senator from Indiana who remains plugged in to national political trends, said the controversy wouldn’t move a lot of voters. But “letting something extraneous like this linger out there, just takes her off message and affects her momentum and who needs that?” he said.

The Warren campaign has sent out a memo with detailed quotes from those involved with her hiring as a professor at Harvard — and the institutions where she taught previously — affirming that she received those positions because she was qualified, not because of her heritage. Warren said she had listed herself as Native American in hopes of attending events with people of similar backgrounds.

Warren’s campaign had no comment for this article.

Brown has called on Warren to release her law school applications from the institutions where she has taught.

Veteran Massachusetts GOP consultant Rob Gray said the issue had the potential to hurt Warren with a key bloc of swing voters if she is seen as having used her ethnic background to get ahead professionally, even if she didn’t.

This “can really cut against a Democrat in Massachusetts. Most of the swing voters available to Republican candidates tend to be less-than-college-educated white voters who have some problems with affirmative action, by and large.”

Back at the gathering of the Massachusetts Teachers Association, which endorsed Warren earlier this year, the support of the crowd for the consumer advocate was palpable.

In her speech, Warren noted her long professional career as an educator and emphasized the fight she’s in.

“I’ve taken the point position,” Warren said. “I’m the teacher who stepped out in front. But I’m counting on the fact that I will not be doing this alone.”

She won’t be.

At a booth set up by her campaign outside the ballroom where she spoke, teachers at the meeting of the 110,000-person union streamed to sign up to help her.

Sharon Bamberg, a special-education teacher in the town of Randolph, was one of those who gave her information to the campaign on Saturday. “She’s one of us,” Bamberg said.

Asked if the Native American issue affected her view of Warren, she dismissed it.

“I don’t care what anyone’s ancestral background is,” Bamberg said. “I’m looking at the person today. She’s intelligent, she pulled herself up, she comes from us: no silver spoon for this lady. She’s a hard worker, and that’s what I really respect.”

Beyond the controversy, the support Warren gets here underscores the mathematical problem Brown faces, no matter how many news cycles he wins. Among Warren’s loyal base of support and beyond, voters in Massachusetts will overwhelmingly vote for President Barack Obama. To win, Brown will need a gigantic number of Obama voters to split their ballot.

“We are aware of the math,” one top Brown campaign aide admitted to Roll Call, “but people in Massachusetts, particularly independents who make up a majority of the electorate, vote for the person, not the party.”

But, Democrats said, if voting the person means voting for a Republican Senate, that might change.

“The key is this,” Rep. Barney Frank (D-Mass.) said, “and this is Scott’s problem — he’s a decent guy, but the more it comes down to who is in control of the Senate, the harder it is for him.”

Gray, the Republican, saw the Native American issue fading from voters’ consciousness unless Brown — or another group — decides to remind Bay Staters of it through paid media.

“It’s only going to matter if someone drives it after Labor Day. I don’t think there’s any long-term damage at this point,” Gray said. “We’re not even to Memorial Day.”